\[\sin{41{^\circ}}\sin{16{^\circ}} =\]
\[= \frac{1}{2} \cdot \left( \cos{25{^\circ}} - \cos{57{^\circ}} \right) =\]
\[= \frac{1}{2}\cos{25{^\circ}} - \frac{1}{2}\cos{57{^\circ}}\]